标题： 贝叶斯多变量模型用于有界方向数据 显示英文标题

标题： Bayesian multivariate models for bounded directional data

摘要： 在某些知识领域中，存在数据表示的方向被限制在特定的数值范围内。 因此，有必要建立用于描述定义在k维单位球子集上的变量的模型。 这种需求促使了如多变量投影伽马分布等模型的发展。 然而，提出其边缘变量仅定义在单位圆的部分区域且具有灵活依赖结构的多变量模型是有限的。 在本工作中，我们提出构建多变量模型，其中每个边缘变量是一个仅定义在单位圆第一象限的循环变量。 我们的方法基于Copula函数的概念。 所提出模型的推断依赖于生成所有涉及模型参数的后验联合密度的样本。 这是通过应用一种条件方法来实现的，该方法允许使用两阶段抽样进行推断。 所提出的这种方法通过模拟数据和实际数据进行了说明。 显示英文摘要

摘要： In some areas of knowledge there are data representing directions restricted to a specific range of values. Consequently, it is useful to have models for describing variables defined in subsets of the k-dimensional unit sphere. This need has led to the development of models such as the multivariate projected Gamma distribution. However, the proposal of multivariate models whose marginal variables are defined only in sections of the unit circle and with a flexible dependency structure is limited. In this work, we propose constructing multivariate models where each marginal variable is a circular variable defined only in the first quadrant of the unit circle. Our approach is based on the concept of copula functions. The inferences for the proposed models rely on generating samples of the posterior joint density of all parameters involved in the models. This is achieved by applying a conditional approach that allows inferences to be made using a two-stage sampling. The proposed methodology is illustrated with both simulated and real data.